Vladimir Putin still has the support of a majority of Russians, his spokesman said on Sunday after a mass protest challenged the premier's authority two months before he stands in presidential polls.

Organisers said 120,000 people attended the rally in central Moscow Saturday where protesters chanted slogans against Prime Minister Putin and called for the annulment of disputed December parliamentary elections won by his party.

Police put the numbers at 29,000 but AFP correspondents said the turnout was clearly bigger and more anti-Putin in tone than the first rally two weeks ago which smashed the taboo in Russia against mass opposition protests.

"As a politician and a presidential candidate, Putin still has the support of a majority. And we should treat the opinion of a majority with respect," his spokesman Dmitry Peskov told AFP.

He added that Putin was "beyond competition" as a candidate in March 4, 2012 presidential polls, where the Russian strongman plans to stand for a third Kremlin term after his four-year stint as prime minister.

Peskov acknowledged the protest had taken place and said the demonstrators' position was to be treated with respect. "Those people who came out onto the streets -- they are a very important part of society. But they are a minority."

The last Soviet leader Mikhail Gorbachev had late Saturday dramatically called on Putin to quit, just as he had done on December 25, 1991 when the USSR collapsed exactly two decades ago.

The protest movement -- which brings together a charismatic anti-corruption blogger, a detective story writer, musicians and a former finance minister -- does not so far have a clear leader but is gaining momentum.

"This is not an outburst which will die down. This is not about the protests but about the mood," Yevgeny Gontmakher, head of the Centre for Social Policies at the Moscow-based Economics Institute, told AFP.

"There is a danger of a revolution. Authorities are making concessions but are not keeping up with the development of the events."

The leaders have not said when the next protest will take place and one of the most prominent opposition figures, politician Vladimir Ryzhkov, admitted that there were "several points of view" within the movement on the timing.

Ryzhkov told Moscow Echo radio he would prefer the next rally to take place in March to coincide with the presidential polls but he said some of his colleagues wanted a rally at the end of January.

The opposition set up a Facebook page (www.facebook.com/moscow.comes.back) to coordinate and debate the timing of future protests.

Another leading figure, 35-year-old blogger Alexei Navalny, provocatively vowed on Saturday that one million people would attend the next anti-Putin rally.

The mass protests were triggered by widespread claim of wholesale violations in this month's parliamentary polls which handed a reduced majority to Putin's ruling United Russia party.

Protesters called for the annulment of the ballot, sacking of the Central Election Commission chief and a re-run of elections.

Hoping to ride out a wave of protests, Putin ignored those demands and promised instead a return to the direct election of regional governors and a simplified procedure to register political parties.

In defiance of the protests, the newly-elected lower house of parliament convened for its first session earlier this week.

Most Russians lost their taste for street politics in the chaotic 90s and the scale of the current protests is a major boon for the fragmented opposition which had for years struggled to encourage Russians to take to the streets.

But incensed by his claims that opposition supporters were in the pay of the US State Department and insults comparing them to an anti-AIDS campaign, protesters are now taking their anger out directly at Putin.